Data structures and load balancing for parallel adaptive hp finite-element methods

Adaptive hp finite-element methods (FEM), in which both grid size h and local polynomial order p are dynamically altered, are very effective discretization schemes for the numerical solution of a large class of partial differential equations. However, these schemes generate computations that require dynamic and irregular patterns of data storage, access, and computation, making their use on multiprocessor machines very difficult. We describe here the development of a suite of data structures and load balancing techniques that addresses these concerns. The central idea is the use of a spatially local ordering of all data and computation using a key generated from geometric data using a space filling curves-based ordering for data storage, distribution, and access. We also evaluate the suitability of tree and table type data structures for adaptive meshing. Example applications and performance data complete the presentation.